Taking a less expensive flight connection may be tempting at first. But, there are risks associated with it and only you can decide if a cheaper airline ticket is worth the risk. Air travel goes smoothly most of the time and hopefully that will be your experience. Using two airlines may make it less likely for you to get helpful customer service assitance if something goes awry.
One scenario where you may need help is in the case of a late or canceled flight. Any airline contracts to get you and your belongings from point "A" to point "B" safe, sound and on time. Airlines are not obligated to help you if you miss a flight or connection because of a delay you faced with another company.
In turn, you are obligated to the terms of each ticket that you purchase with each airline. Less expensive tickets may have restrictions that prohibit you from making changes after booking. If you miss connections because of a flight delay from another company, then you may lose your ticket money and have to rebook at a higher price.
Bags are normally transported from one connection to another for you when traveling with a single airline. You are on you own to deal with your bags when using two different companies. Make sure that there is ample time between connections to collect your luggage and make it to the connecting airline well in advance of your flight. If you don't have enough time, then you may have to decide between picking up a suitcase or missing a flight.
Customer loyalty rewards may be another complication. Each airline has its own system for qualifying and retaining rewards. Booking with a second airline will likely take away from the points you would receive by using a single company. This is comparativly minor, but if you are trying to collect points for a certain goal, then it is worth consideration.
Only you can decide if the cost savings is worth the risk. Researching all the options is the only way to determine if using two carriers is right for you.